Homework: 2.2 Organizing Quantitative Data and Skewness

Determine the original set of data. 1 | 017 2 | 14478 3 | 355578 4 | 01 The original set of data is ___________________________

10, 11, 17, 21, 24, 24, 27, 28, 33, 35, 35, 35, 37, 38, 40, 41

Determine the original set of data. 14 | 5 8 8 9 15 | 0 3 4 6 8 9 9 16 | 3 5 5 7 7 8 8 17 | 1 3 3 6 8 18 | 0 3 ​Legend: 5|2 represents 5.2

14.5​, 14.8​, 14.8​, 14.9​, 15.0​, 15.3​, 15.4​, 15.6​, 15.8​, 15.9​, 15.9​, 16.3​, 16.5​, 16.5​, 16.7​, 16.7​, 16.8​, 16.8​, 17.1​, 17.3​, 17.3​, 17.6​, 17.8​, 18.0​, 18.3

_________are the categories by which data are grouped.

Classes

A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtains the data in the accompanying table. 1 3 2 2 1 2 1 3 3 2 1 3 2 1 3 2 2 1 1 3 1 1 2 2 3 2 0 1 4 5 2 1 2 3 2 1 1 2 2 3 (a) Are these data discrete or​ continuous? Explain. (b) Construct a frequency distribution of the data. (c) Construct a relative frequency distribution of the data. (d)What percentage of households in the survey have three​ televisions? (e) What percentage of households in the survey have four or more​ televisions? (f) Construct a frequency histogram of the data. Choose the correct graph below. (g) Construct a relative frequency histogram of the data. Choose the correct graph below. (f) Describe the shape of the distribution. The distribution is ____________

(a) A. The given data are discrete because they can only have whole number values. (b) 1, 13, 15, 9, 1, 1 (c) .025, .325, .375, .025,.025 (d) 22.5 (e) 5 (f) A (g) B (h) skewed right.

true or false: ​Stem-and-leaf plots are particularly useful for large sets of data.

False

True or false: The shape of the distribution shown is best classified as uniform. O OOO OOOOO OOOOOOO OOOOOOOOO

False - it is bell shaped

For ages of hearing-aid patients​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right.

Skewed left

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be​ larger, the mean or the​ median? Why? Choose the correct answer below. A. The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail. B. The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail. C. The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail. D. The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail.

B. The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.

The​ _________________ is the difference between consecutive lower class limits.

class width

To predict future enrollment in a school​ district, fifty households within the district were​ sampled, and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table. Number of Children under 5 Number of Households 0 13 1 16 2 15 3 3 4 3 Construct a relative frequency distribution of the data. Number of Children under 5 Relative Frequency 0 _______ 1 _______ 2 _______ 3 _______ 4 _______ ​(b) What percentage of households has two children under the age of​ 5? ​(c) What percentage of households has one or two children under the age of​ 5?

(a) . 26 . 32 . 3 . 06 . 06 (b) 30​% (c) 62​%

True or false: The shape of the distribution shown is best classified as skewed left. o o o o o o ooooo ooooooo oooooooo oooooooooo

False it is skewed right

The​ ______ class limit is the smallest value within the class and the​ ______ class limit is the largest value within the class.

lower, upper

The histogram on the right represents the connection time in seconds to an internet provider. Determine which measure of central tendency better describes the​ "center" of the distribution. What measure of central tendency best describes the​ "center" of the​ distribution? mode median mean

mean

An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The frequency histogram to the right gives the results. (a) What was the most frequent outcome of the​ experiment? (b) What was the least​ frequent? ​(c) How many times did we observe a 6​? ​(d) How many more 7​'s were observed than 3​'s? ​(e) Determine the percentage of time a 6 was observed. ​(f) Describe the shape of the distribution. Choose the correct answer below.

(a) 9 (b) 2 (c) 13 (d) 9 (e) 13 (f) bell shaped

A survey recently went out to 15 university presidents across a certain country. The data represents the ages of the different presidents. Use a​ stem-and-leaf plot that has two rows for each stem to represent their ages. 52​, 64​, 59​, 50​, 57​, 59​, 62​, 68​, 56​, 63​, 50​, 64​, 56​, 51​, 72 Determine the leaves in the​ stem-and-leaf plot. Stem Leaves 5 | ________ 5 | ________ 6 | ________ 6 | ________ 7 | ________ Which of the following best summarizes what the​ stem-and-leaf plot tells you about the​ data? A. The plot shows that most university presidents have ages that range from 50 to 65 years old. B. The plot shows that there is an equal amount of university presidents under the age of 60 as there is above the age of 60. C. The plot shows that the age of the university presidents cluster around age 60. D. The plot shows that most university presidents have ages that range from 65 to 75 years old.

0012 66799 2344 8 2 A. The plot shows that most university presidents have ages that range from 50 to 65 years old.

What is a disadvantage of using a​ stem-and-leaf plot instead of a​ histogram? A. Histograms easily organize data of all sizes where​ stem-and-leaf plots do not. B. Histograms show data clusters where​ stem-and-leaf plots do not. C. Histograms contain original data values where​ stem-and-leaf plots do not. D. Histograms graph quantitative data where​ stem-and-leaf plots do not.

A. Histograms easily organize data of all sizes where​ stem-and-leaf plots do not.

What is an advantage of using a​ stem-and-leaf plot instead of a​ histogram? A. ​Stem-and-leaf plots easily organize data of all sizes where histograms do not. B. ​Stem-and-leaf plots contain original data values where histograms do not. C. ​Stem-and-leaf plots graph qualitative data where histograms do not. D. ​Stem-and-leaf plots show data clusters where histograms do not.

B. ​Stem-and-leaf plots contain original data values where histograms do not.

The following frequency histogram represents the IQ scores of a random sample of​ seventh-grade students. IQs are measured to the nearest whole number. The frequency of each class is labeled above each rectangle. (a) How many students were​ sampled? ​(b) Determine the class width. The class width is ______ ​(c) Identify the classes and their frequencies. Choose the correct answer below. A. ​65, 1​; ​75, 4​; ​85, 13​; ​95, 41​; ​105, 60​; ​115, 40​; ​125, 29​; ​135, 8​; ​145, 2​; ​155, 2 B. ​60-69, 1​; ​70-79, 4​; ​80-89, 13​; ​90-99, 41​; ​100-109, 60​; ​110-119, 40​; ​120-129, 29 ; ​130-139, 8​; ​140-149, 2​; ​150-159, 2 C. ​60-70, 1​; ​70-80, 4​; ​80-90, 13​; ​90-100, 41​; ​100-110, 60​; ​110-120, 40​; ​120-130, 29 ; ​130-140, 8​; ​140-150, 2​; ​150-160, 2 ​(d)Which class has the highest​ frequency? A. 105 B. 90-99 C. 100-110 D. 100-109 ​(e) Which class has the lowest​ frequency? A. 65 B. 60-69 C. 150 -159 D. 60-70 ​(f) What percent of students had an IQ of at least 130? ​(g) Did any students have an IQ of 161​? A. ​No, because there is a bar in the​ 150-159 class. B. ​Yes, because there is a bar in the​ 150-159 class. C. ​No, because there are no​ bars, or​ frequencies, greater than an IQ of 160. D. ​Yes, because there is a frequency of a score of 165.

(a) 200 (b) 10 (c) B. ​60-69, 1​; ​70-79, 4​; ​80-89, 13​; ​90-99, 41​; ​100-109, 60​; ​110-119, 40​; ​120-129, 29 ; ​130-139, 8​; ​140-149, 2​; ​150-159, 2 (d) D. 100-109 (e) B. 60-69 (f) 6​% ​ (g) C. ​No, because there are no​ bars, or​ frequencies, greater than an IQ of 160.

The U.S. Department of Housing and Urban Development​ (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the​ median? A. HUD uses the median because the data are skewed right. B. HUD uses the median because the data are bimodal. C. HUD uses the median because the data are skewed left. D. HUD uses the median because the data are symmetrical.

A. HUD uses the median because the data are skewed right.

The letters​ A, B, and C are marked on the histogram. Describe the shape of the data. Then determine which is the​ mean, which is the​ median, and which is the mode. Justify your answers. Which description below best describes the shape of the​ distribution? Uniform Symmetric Skewed right Skewed left In this​ distribution, how is the mode​ determined? A. The​ mean, median, and mode are all equal. B. The mode cannot be identified. C. The mode is the data entry that has the highest frequency. D. The mode is the data entry that has the lowest frequency. The mode is labeled ___? C. In this​ distribution, how is the mean​ determined? A. The mean is to the right of the median and mode. B. The​ mean, median, and mode are all equal. C. The mean cannot be identified. D. The mean is to the left of the median and mode. The mean is labeled ___? In this​ distribution, how is the median​ determined? A. The​ mean, median, and mode are all equal. B. The median is to the left of the mean and to the right of the mode. C. The median is to the right of the mean and to the left of the mode. D. The median cannot be identified. The median is labeled ___?

Skewed left C. The mode is the data entry that has the highest frequency. C D. The mean is to the left of the median and mode. A C. The median is to the right of the mean and to the left of the mode. B